Laser-focused nanofabrication: Beating of two atomic resonances

E. Jurdik, J. Hohlfeld, H. van Kempen and Th. Rasing

NSRIM, University of Nijmegen,

Toernooiveld 1, 6525 ED Nijmegen, the Netherlands

J.J. McClelland

Electron Physics Group, National Institute of Standards and Technology,

Gaithersburg, Maryland 20899-8412

(February 25, 2002)

Abstract

We deposit a laser-collimated chromium beam onto a substrate through a

laser standing-wave (SW) tuned above the atomic resonance at either of the

two 52Cr transitions 7S3 → 7P o3 at 427.600 nm or 7S3 → 7P o

4 at 425.553 nm.

In both these cases the resulting pattern on the surface consists of nanolines

with a period of that of the SW. We extend the range of periods accessible

to laser-focused atom deposition by superimposing the structures grown at

both these resonances. The resulting beating pattern exhibits a period of

44.46 ± 0.04 µm as determined with a polarizing optical microscope. This

structure provides a link between nanoscopic and macroscopic worlds and

could potentially become a calibration standard for length metrology.

PACS number(s): 42.50.Vk, 03.75.Be, 81.16.-c, 06.20.-f

Typeset using REVTEX

1

Atoms from an atom beam, when they interact with a far-off-resonant laser standing-

wave (SW), experience a spatially varying potential with a period of that of the SW [1].

Depending on whether the laser frequency is tuned above or below an atomic resonance, the

potential minima are either located in the troughs or crests of the light intensity, respectively.

As the atoms pass through a potential minimum in the SW, they experience a focusing action

similar to what light experiences in a lens. A laser SW can therefore be used to focus an

atom beam into an array of lines or dots. A substrate can then be placed into the modulated

atom beam and, by so doing, nanostructures can be grown.

The first demonstration of this use of light for direct writing with atoms was done by

Timp et al. [2] who reported experiments with neutral sodium atoms. Subsequently, Mc-

Clelland et al. [3] produced chromium nanostructures. Later, Gupta et al. [4] demonstrated

that a square-lattice of equidistantly spaced features can be produced by superimposing two

laser SW’s at a normal angle. Drodofsky et al. [5] fabricated nanostructures with a hexag-

onal symmetry by crossing three laser beams at mutual angles of 120o. Also, aluminum [6],

directly, and cesium [7], via lithography with a self-assembled monolayer as the resist, were

used for making nanolines. More complicated periodic patterns may be written by moving

the substrate or by using more complex laser field patterns. The latter approach has been

adopted recently. Gupta et al. [8], when working with two counter-propagating laser beams

with mutually orthogonal linear polarizations, fabricated lines with a period of λ/8. Brezger

et al. [9] extended this polarization-gradient approach to two dimensions.

In this letter, we describe an experiment with a chromium beam that is focused in a one-

dimensional laser SW to form periodic nanolines. In addition to the 7S3 → 7P o4 (J = 3 → 4)

transition of the dominant isotope 52Cr at a vacuum wavelength of 425.553 nm that has been

employed in all atom-optical experiments with chromium so far [3–5,8,9], we also make use

of the 7S3 → 7P o3 (J = 3 → 3) transition at 427.600 nm. After demonstrating laser-focused

nanofabrication at both these resonances separately, we fabricate a beating pattern with a

measured period of 44.46 ± 0.04 µm by subsequent depositions onto the same pad on the

substrate.

2

For the experiment presented here, laser light tunable around 425 nm was obtained by

frequency doubling the output of a titanium-doped sapphire laser in an external enhance-

ment doubling cavity [10]. The chromium beam was produced from a high-temperature

effusion cell held at 1900 K. It was subsequently collimated by means of laser cooling [11]

to reduce the transverse velocity spread of the atoms. The full width at half-maximum

(FWHM) divergence angle following laser collimation of the atom beam was 0.5–0.6 mrad

for depositions at J = 3 → 3 and 0.2–0.3 mrad for those at J = 3 → 4 [12]. This laser-

collimated beam was deposited through a laser SW, which was tuned 200 MHz above the

involved atomic transition by an acousto-optical modulator, onto a glass substrate coated

with a 100 nm thick layer of indium tin oxide (ITO). In spite of the fact that its surface is

somewhat granular, ITO was chosen because of its conductivity (required for eventual elec-

tron microscopy studies) and optical transparency. Three patches of chromium nanolines

with an approximate size of 1.5 mm across and 0.5 mm along the lines were grown onto

the substrate. The first and second depositions were carried out at the J = 3 → 3 and

J = 3 → 4 transitions, respectively, and lasted for 7 minutes (corresponding to an average

film thickness of roughly 3 nm). The third patch is a result of subsequent depositions at

the two respective transitions. The deposition time was 7 minutes for each transition. The

laser SW was created upon retro-reflection of a Gaussian laser beam from an in vacuo mir-

ror. This laser beam was focused to a 1/e2 intensity radius of approximately 100 µm and

contained a power of 25 ± 3 mW for depositions at J = 3 → 3 and 15 ± 2 mW for those at

J = 3 → 4 [13]. The polarization of the SW beam was linear and normal to the substrate

surface, which was located at the center of the SW beam and was parallel to it to within

0.2 mrad. During depositions the vacuum pressure was about 10−5 Pa (10−7 mbar).

Atomic force microscope (AFM) images of the structures grown at J = 3 → 3 and

J = 3 → 4 are shown in Figs. 1(a) and (b), respectively. Although the surface appears fairly

rough because of ITO grains, periodic modulation due to laser-focused chromium is clearly

present. In order to obtain the structure profile, the raw AFM data were averaged over

2 µm along the lines. These profiles are shown in the insets of Fig. 1. The FWHM structure

3

width (measured above the background) is 70–80 nm for the deposition at J = 3 → 3 and

35–40 nm for that at J = 3 → 4. The difference in the widths (a factor of 2) is commensurate

with the difference in the FWHM divergence angles of the atom beam for the two respective

depositions. This result can be explained by analogy with optical imagery: the image size of

a distant object scales linearly with the divergence of the light entering the imaging system

[14].

The structures from Figs. 1(a) and (b) exhibit a period of λ/2, where λ = 427.600 nm

and 425.553 nm, respectively. Therefore, slow modulation with a period Λ = 44.45 µm

is expected when these two structures are superimposed by subsequent depositions. In

Figs. 2(a) and (b) AFM images of the beating pattern obtained in this manner are shown.

These two AFM scans were displaced by approximately 21 µm measured across the lines.

They represent areas where the two SW’s were nearly out-of-phase and nearly in-phase,

respectively. This is more clearly demonstrated by the insets in Figs. 2(a) and (b) that show

the structure profile averaged over 2 µm along the lines. We note that the beating pattern

from Fig. 2 is not a result of simple addition of the two structures from Fig. 1. This may

be due to surface growth and diffusion effects that cause feature broadening for increased

coverage [15].

An image of the beating sample placed at 45o between a polarizer and a crossed analyzer

in a transmission optical microscope with white light illumination is shown in Fig. 2(c). The

sample appears as a periodic pattern of alternating dark and bright stripes because laser-

focused nanolines act as a polarizer with extinction capability on the order of 1%. They are

for light somewhat similar to what a grating polarizer is for far-infrared and radio waves

[16]. In order to demonstrate the polarizing action, we measured the light intensity I(ϕ)

in the minima and maxima of the beating pattern as a function of the sample’s azimuthal

angle ϕ. The result is shown in Fig. 3. It is seen that I(ϕ) follows the expected dependence

I(ϕ) ∝ sin2(2ϕ).

We determined the average beating period Λ as follows. First, the relative uncertainty

of Λ across the whole 1.5 × 0.5 mm chromium patch was evaluated to 0.05%. Second, the

4

distance 26Λ was determined to 1156 ± 1 µm by making use of a calibration standard – a

lithography mask with two strip-lines separated by 1171±1 µm (note that the measurement

uncertainty was negligible compared with the stated uncertainty of the artifact). These

results then imply Λ = 44.46 ± 0.04 µm. Within the indicated uncertainty, this period

agrees with our expectation of 44.45 µm. We note here that the above stated uncertainty

of the beating period is instrumental; it is linked to the accuracy of our measurement tools

– the lithography mask as well as the microscope camera. We believe the accuracy of the

period may be much higher than this. Preliminary theoretical considerations indicate an

uncertainty of the average pitch of chromium nanolines in the range of 40 ppm (parts-

per-million) [17]. This uncertainty is largely systematic, being due to misalignment of the

experiment, characteristics of both the atom beam and the SW laser beam, and mechanical

as well as thermal properties of the substrate material. Assuming this uncertainty for the

nanolines and making the reasonable assumption that both depositions are subject to the

same systematic error, we anticipate an uncertainty of better than 50 ppm (corresponding

to 2 nm) for the beating period. It should be emphasized, however, that a more thorough

investigation is required to completely explore the error budget and to determine the true

uncertainty of all the three involved periods.

In conclusion, we have demonstrated laser-focused nanofabrication with a chromium

beam at the two transitions from the atomic ground state of 52Cr, 7S3, to both the 7P o3

and 7P o4 excited states at 427.600 nm and 425.553 nm, respectively. We have shown that

subsequent depositions onto the same pad on the substrate result in a beating pattern with a

measured period of 44.46± 0.04 µm. It is clearly resolved by both an AFM and a polarizing

optical microscope. In the latter case, a highly uniform, periodic light intensity profile indi-

cates extreme coherence of the deposition process. This feature of the technique, combined

with the fact that the frequency of the SW is strictly referenced to an atomic resonance,

makes laser-focused nanolines attractive for length metrology. The patterning by beating

of two atomic resonances then provides the means of extending the laser-focused nanofab-

rication technique to large periods, while still maintaining nanoscale surface modulation.

5

A single sample could hence be applied for calibration of a wide variety of microscopies,

ranging from scanning-probe to electron to optical.

The authors would like to thank A. van Etteger, A. Toonen, J. Hermsen, P. Dolron and

R. van Dongen for invaluable technical assistance. Part of this work was supported by the

Stichting voor Fundamenteel Onderzoek der Materie (FOM), which is financially supported

by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO).

6

REFERENCES

[1] J.P. Gordon and A. Ashkin, Phys. Rev. A 21, 1606 (1980).

[2] G. Timp, R.E. Behringer, D.M. Tennant, J.E. Cunningham, M. Prentiss, and

K.K. Berggren, Phys. Rev. Lett. 69, 1636 (1992).

[3] J.J. McClelland, R.E. Scholten, E.C. Palm, and R.J. Celotta, Science 262, 877 (1993).

[4] R. Gupta, J.J. McClelland, Z.J. Jabbour, and R.J. Celotta, Appl. Phys. Lett. 67, 1378

(1995).

[5] U. Drodofsky, J. Stuhler, Th. Schulze, M. Drewsen, B. Brezger, T. Pfau, and J. Mlynek,

Appl. Phys. B 65, 755 (1997).

[6] R.W. McGowan, D.M. Giltner, and S.A. Lee, Opt. Lett. 20, 2535 (1995).

[7] F. Lison, H.-J. Adams, D. Haubrich, M. Kreis, S. Nowak, and D. Meschede, Appl. Phys.

B 65, 419 (1997).

[8] R. Gupta, J.J. McClelland, P. Marte, and R.J. Celotta, Phys. Rev. Lett. 76, 4689

(1996).

[9] B. Brezger, Th. Schulze, P.O. Schmidt, R. Mertens, T. Pfau, and J. Mlynek, Europhys.

Lett. 46, 148 (1999).

[10] E. Jurdik, J. Hohlfeld, A.F. van Etteger, A.J. Toonen, W.L. Meerts, H. van Kempen,

and Th. Rasing, J. Opt. Soc. Am. B, in press.

[11] H.J. Metcalf and P. van der Straten, Laser cooling and trapping, 1st ed. (Springer-Verlag,

Berlin, 1999).

[12] The difference between the collimation results for the two transitions can be explained as

follows. The J = 3 → 4 transition is ideal for laser manipulation because no population

traps are produced during laser cooling. The situation is, however, different for cooling

at J = 3 → 3. The atoms can be optically pumped into magnetic sublevels that do

7

not couple to the local laser field anymore. While in the former case the cooling was

due to the well-known Sisyphus polarization gradient scheme, in the latter case a non-

zero magnetic field was applied in the cooling region and we therefore anticipate a

magnetically-induced laser cooling mechanism (for details, see [11]).

[13] Unless otherwise specified, all quoted uncertainties are intended to be interpreted as

one standard deviation combined random and systematic errors.

[14] J.J. McClelland, J. Opt. Soc. Am. B 12, 1761 (1995).

[15] E. Jurdik, Th. Rasing, H. van Kempen, C.C. Bradley, and J.J. McClelland, Phys. Rev.

B 60, 1543 (1999).

[16] H.E. Bennett and J.M. Bennett, “Polarization,” in Handbook of Optics, edited by W.G.

Driscoll and W. Vaughan, 1st ed. (McGraw-Hill, New York, 1978, pp. 10-1–10-164).

[17] J.J. McClelland, unpublished.

8

FIGURES

FIG. 1. AFM scans of laser-focused Cr nanolines on an ITO substrate. Depositions carried out

at the J = 3 → 3 (a) and J = 3 → 4 (b) transitions. Insets: Profiles averaged over 2 µm along the

lines.

FIG. 2. Superimposed depositions at the J = 3 → 3 and J = 3 → 4 transitions. (a), (b) AFM

scans at the nearly out-of-phase (a) and nearly in-phase (b) regions. Insets in (a), (b): Profiles

averaged over 2 µm along the lines. (c) Optical microscope image obtained in transmission. The

sample was placed at 45o between a polarizer and a crossed analyzer. Inset in (c): Intensity profile

averaged over 0.3 mm along the lines.

FIG. 3. Analysis of the beating pattern in a transmission optical microscope. The sample was

placed between a polarizer and a crossed analyzer. Light intensity I(ϕ) at the in-phase (intensity

maxima) and out-of-phase (intensity minima) regions as a function of the sample’s azimuth ϕ.

Squares – data points, lines – I(ϕ) ∝ sin2(2ϕ).

9

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